A choke coil is needed to operate an arc lamp at 160 V (rms) and 50 Hz. The lamp has an effective resistance of `5 Omega` when running at 10 A (rms). Calculate the inductance of the choke coil. If the same arc lamp is to be operated on 160 V (DC), what additionalresistance is required ? Compare the power loses in both cases.

Explanation

We know that`i_(rms)=(V_(rms))/(sqrt(R^(2)+omega^(2)L^(2)))`[in series RL AC circuit)
`therefore10=(160)/(sqrt(25+(2pixx50xxL)^(2)))`
`or25+(100piL)^(2)=16^(2)`
`implies25+10^(5)L^(2)=256impliesL=sqrt(231)/(10^(5))=0.05H`Let `R_(A)` be the additional resistance required for operating the arc lamp with 160-V DC source, then `10=sqrt((160)/(R_(A)+5))impliesR_(A)+5=16`
`thereforeR_(A)=16-5=11Omega`
AC power consumed by the arc lamp =`V_(rms)I_(rms)cosphi=P_(ac)`
wherecosphi`=(R)/(Z)=(R)/(sqrt(R^(2)+(omegaL)^(2)))=(5)/(16)`
`impliesP_(ac)=160xx10xx(5)/(16)=500W`
Now, DC power consumed by arc lamp`P_(dc)=160xx10=1600W`
Power loss = 1600 - 500 = 1100 W = 68.75%